The value of sin^2 frac{pi}{8} + sin^2 frac{3 | vedclass

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(B) We know that $\sin(\pi - 	heta) = \sin 	heta$.Therefore,$\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$ and $\sin \frac{5

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$2$

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(B) We know that $\sin(\pi - 	heta) = \sin 	heta$.Therefore,$\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$ and $\sin \frac{5\pi}{8} = \sin(\pi - \frac{3\pi}{8}) = \sin \frac{3\pi}{8}$.The given expression becomes: $2 \sin^2 \frac{\pi}{8} + 2 \sin^2 \frac{3\pi}{8} = 2 [\sin^2 \frac{\pi}{8} + \sin^2 \frac{3\pi}{8}]$.Since $\sin \frac{3\pi}{8} = \sin(\frac{\pi}{2} - \frac{\pi}{8}) = \cos \frac{\pi}{8}$,we have $\sin^2 \frac{3\pi}{8} = \cos^2 \frac{\pi}{8}$.Substituting this into the expression: $2 [\sin^2 \frac{\pi}{8} + \cos^2 \frac{\pi}{8}] = 2(1) = 2$.

The value of $\sin^2 \frac{\pi}{8} + \sin^2 \frac{3\pi}{8} + \sin^2 \frac{5\pi}{8} + \sin^2 \frac{7\pi}{8}$ is

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